Scattering theory for the wave equation on a hyperbolic manifold (Q1110736)

This paper deals with the spectrum of the perturbed Laplace-Beltrami operator acting on automorphic functions in n-dimensional real hyperbolic space. The discrete subgroup is assumed to have the finite geometric property but is otherwise not restricted. The approach uses the non- Euclidean wave equation and relies on the translation representation for the unperturbed system which was developed by Lax and Phillips. It is shown for short-range perturbations that the wave operators exist and are complete.